Non-linear stability analysis of $\ell$-Proca stars

TL;DR

This paper performs a comprehensive non-linear stability analysis of $oldsymbol{ extit{ extcolor{blue}{ ext{l}}}}$-Proca stars, revealing their instability and the emergence of complex multi-field configurations through advanced numerical simulations.

Contribution

It introduces a detailed non-linear stability study of $oldsymbol{ extit{ extcolor{blue}{ ext{l}}}}$-Proca stars with $oldsymbol{ extit{ extcolor{blue}{ ext{l}}}=2}$, demonstrating their instability and transition to multi-$oldsymbol{ extit{ extcolor{blue}{ ext{l}}}}$ configurations.

Findings

$oldsymbol{ extit{ extcolor{blue}{ ext{l}}}}=2$-Proca stars are unstable across their entire existence.

Less compact stars develop non-axisymmetric instabilities.

Unstable stars migrate to multi-$oldsymbol{ extit{ extcolor{blue}{ ext{l}}}}$ Proca stars with mixed angular momentum modes.

Abstract

Vector boson stars, also known as Proca stars, exhibit remarkable dynamical robustness, making them strong candidates for potential astrophysical exotic compact objects. In search of theoretically well-motivated Proca star models, we recently introduced the $\ell$-Proca star, a multi-field extension of the spherical Proca star, whose $(2\ell + 1)$ constitutive fields have the same time and radial dependence, and their angular structure is given by all the available spherical harmonics for a fixed angular momentum number $\ell$. In this work, we conduct a non-linear stability analysis of these stars by numerically solving the Einstein-(multi, complex) Proca system for the case of $\ell = 2$, which are formed by five constitutive independent, complex Proca fields with $m = 0, |1|$, and $|2|$. Our analysis is based on long-term, fully non-linear, 3-dimensional numerical-relativity simulations without imposing any symmetry. We find that ($\ell=2$)-Proca stars are unstable throughout their entire domain of existence. In particular, we highlight that less compact configurations dynamically lose their global spherical symmetry, developing a non-axisymmetric $\tilde{m}=4$ mode instability and a subsequent migration into a new kind of multi-field Proca star formed by fields with different angular momentum number, $\ell=1$ and $\ell=2$, that we identify as unstable multi-$\ell$ Proca stars.